Using derivatives, it is found that regarding the tangent line to the function, we have that:
- The equation of the line is y = 962x - 5119.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:
f(x) = 5x³ + 2x + 1.
The derivative is given by:
f'(x) = 15x² + 2.
Hence the slope at x = 8 is:
m = f'(8) = 15(8)² + 2 = 962.
The line goes through the point (8,f(8)), hence:
f(8) = 5(8)³ + 2(8) + 1 = 2577.
Hence:
y = 962x + b
2577 = 962(8) + b
b = -5119.
Hence the equation is:
y = 962x - 5119.
More can be learned about tangent lines at brainly.com/question/8174665
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360 outfits i think i wouldnt take that as fact tho
Answer: B
Step-by-step explanation:
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. Since the machines are identical and running at the same constant rate, it means each of them as the same rate. The rate of each machine can produce would be determined by dividing the combined unit rate by 6. It becomes
270/6 = 45 bottles per minutes
The rate for 10 machines running at the same constant rate would be
10 × 45 = 450 bottles per minutes.
If the 10 machines produce 450 bottles per minutes, then,
In 4 minutes, the 10 machines will produce 4 × 450 = 1800 bottles
Answer:
Your sum = 
- 1
S = ( (-2)^n - 1), If you let n = z, then S = (-2)^z - 1
Step-by-step explanation:
I can use a formula to find the sum of the first n terms.
we have -3, 6, -12, 24, ... etc.
common ratio = r = -2
first term = -3
a_1 = -3
Then: a_n = a_1 * r ^(n -1)
a_n = (-3) * (-2)^(n - 1) is the general formula for the nth term
Sum of first n terms = S = a_1 * (r^n - 1) / (r - 1)
so...
S = (-3) * ((-2)^n - 1 )/ (-2 - 1)
which simplifies to
S = (-3) *((-2)^n - 1) / (-3)
S = ( (-2)^n - 1)
If you let n = z, then S = (-2)^z - 1
